Question:
In a central difference table, which of the following is correct?
In a central difference table, which of the following is correct?
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Compare how the origin is chosen in forward, backward, and central difference tables.
Updated On: Jul 4, 2026
- The origin \(x_0\) is the first argument in the series.
- The origin \(x_0\) is the last argument in the series.
- The origin \(x_0\) is the intermediary value in the series.
- The origin \(x_0\) is the equal distance from the first and last arguments of the series.
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The Correct Option is C
Solution and Explanation
Step 1: Recall the three standard difference tables used in numerical interpolation. In a forward difference table, the origin \(x_0\) is taken as the first tabulated argument, used in Newton's forward interpolation formula for values near the start of the table.
Step 2: In a backward difference table, the origin \(x_0\) is taken as the last tabulated argument, used in Newton's backward interpolation formula for values near the end of the table.
Step 3: In a central difference table, the origin \(x_0\) is instead chosen at some interior, intermediary point of the tabulated data, so interpolation can be carried out accurately for values lying near that interior point, as in Gauss's, Stirling's, and Bessel's central difference formulas.
Step 4: Options (A) and (B) describe the forward and backward difference tables, not the central one. Option (D) wrongly demands the origin be exactly equidistant from both ends, which is more restrictive than what actually defines a central difference table; only an interior/intermediary position is required. So the correct description is option (C).
\[\boxed{\text{The origin } x_0 \text{ is the intermediary value in the series}}\]Was this answer helpful?
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